Three-dimensional surfaces are often represented in computer memory by a contiguous collection of tiles, such as triangular tiles. Such a representation may be referred to as a “tesselation” or a “mesh.”
A “geodesic distance,” with respect to a given surface, between two points that lie on the surface, is the length of the shortest path, along the surface, that connects the two points. For points lying on a curved surface, this distance is often different from the Euclidean distance between the points. For example, the geodesic distance between two hilltops is the length of the shortest path that runs, along the surface of the Earth, between the two hilltops. This distance is larger than the Euclidean distance between the hilltops, which is the length of a straight path, through the air, passing between the hilltops.